Print your name and section clearly on all nine
pages. (If you do not know your section number, write your
TA's name.) Show all work in the space immediately below each
problem. Your final answer must be placed in the box provided.
Problems will be graded on reasoning and intermediate steps as
well as on the final answer. Be sure to include units wherever
necessary, and the direction of vectors. Each problem is worth
25 points. In doing the problems, try to be neat. Check
your answers to see that they have the correct dimensions (units)
and are the right order of magnitude. You are allowed one 8.5
x 11 sheet and no other references. The exam lasts exactly
two hours.

(Do not write below)

SCORE:

Problem 1: __________

Problem 2: __________

Problem 3: __________

Problem 4: __________

Problem 5: __________

Problem 6: __________

Problem 7: __________

Problem 8: __________

TOTAL: ___________

Possibly useful information:

Acceleration due to gravity at the earth's surface: g =
9.80 m/s2

Gravitational constant: G = 6.67 x 10-11 N·m2/kg2

Gas Constant: R = 8.31 J(mol-1)K-1

PROBLEM 1

A bullet leaves the muzzle of a gun 2 meters above the level ground
traveling horizontally. It strikes the ground 600 meters away.
Ignore air resistance in your answers to the following:

a. For how much time was the bullet in flight? (5 pts.)

b. What was the speed of the bullet when it left the gun? (5
pts.)

c. At what angle from the horizontal did the bullet strike the
ground? (5 pts.)

d. What is the ratio of kinetic to potential energy (relative
to the ground) of the bullet when it was fired? (5 pts.)

e. If the gun barrel was 70 cm long, what was the (assumed constant)
acceleration of the bullet while it was in the gun barrel? (5
pts.)

PROBLEM 2

A 2-kg block is connected by a string to a 1-kg block, and they
both slide down a plane inclined at an angle of 30. The lower
(2-kg) block has no friction, and the upper (1-kg) block has
= 0.6.

a. What is the magnitude of the acceleration of the blocks? (15
pts.)

b. What is the tension in the string? (10 pts.)

PROBLEM 3

A block of mass 680 g is attached to a spring with spring constant
65 N/m. It is pulled a distance 11 cm away from its equilibrium
position.

a. What is the period of oscillation? (5 pts.)

b. What is the maximum speed of the block? (5 pts.)

c. What is the maximum acceleration of the block? (5 pts.)

d. What is the potential energy of the block when it is 5.5 cm
from equilibrium? (5 pts.)

e. What is the kinetic energy of the block when it is 5.5 cm
from equilibrium? (5 pts.)

PROBLEM 4

A 100-kg car traveling 20 m/s collides head-on with a 2000-kg
truck initially at rest, and the car rebounds with a speed of
4 m/s in the opposite direction.

a. What is the speed of the truck just after the collision? (5
pts.)

b. What is the magnitude of the impulse on the car? (5 pts.)

c. If the collision lasts 0.4 seconds, what is the average deceleration
of the car? (5 pts.)

d. What fraction of the kinetic energy is lost in the collision?
(5 pts.)

e. Where does the kinetic energy lost in the collision go? (5
pts.)

PROBLEM 5

A 3-kg circular ring is released from rest from the top of a 1-m-high
ramp inclined at an angle of 20 and rolls down the ramp without
slipping.

a. What is the total kinetic energy of the ring when it reaches
the bottom of the ramp? (5 pts.)

b. What fraction of this energy is in translation of the center
of mass? (5 pts.)

c. What is the speed of the center of mass when the ring reaches
the bottom of the ramp? (5 pts.)

d. What is the magnitude of the acceleration of the center of
mass while the ring is rolling down the ramp? (5 pts.)

e. How much time does it take for the ring to reach the bottom
of the ramp? (5 pts.)

PROBLEM 6

One proposal for a manned mission to Mars is to assemble a space
station in earth orbit from which a mission would be launched.

a. Given that the radius of the earth is Re = 6370 km,
use the information on the cover page to calculate the mass of
the earth. (5 pts.)

b. Calculate the work required to place a 1-kg mass into a circular
low-earth (h << Re) orbit. (10 pts.)

c. Calculate the additional work required for the 1-kg
mass above to escape completely from the earth's gravity. (10
pts.)